Reason’s Reasoning · Maclain Hunter

Authored by Maclain Hunter · first-party-authored · authored-foundational-record

Stored 4P source diagnostic: clear · finding no_violation_detected · admission admitted_provisionally. This intake result is separate from the theorem checks of the exact propositional sequent.

Reason’s Reasoning by Maclain Hunter Premises: P: Logos (Reason) and non-contradiction of Logic. Q: Coherent engagement with/between Reason and reasoning (including Reason and Reason’s own reasoning in the absolute sense; including “neosis neoseos” ala Aristotle). R: Reasoning without contradiction, engaging Logic/Logos (by Logos or contingent minds). S: Assume different permutations of {P, Q, R} being true or false. Only P, Q, and R all being true ends in the Coherence of Reason, reasoning, and coherent engagement. If P is True but Q and R are false, or any similar combination, the incoherence tautologically arises between Reason, reasoning, and rational engagement - which is untenable. T: Premise S and its reductio show that P, Q, and R must be true, not for merely the sake of this proof or a personal belief, but for the general and transcendental Coherence of Reason, reasoning, and rational engagement. Proof: {P, P -> Q, P -> R, P -> (Q <-> R), S, S -> T, T -> ((P & Q) & R)} |= P <-> (Q <-> R) Conclusion: {P, Q, R, S, T}: The reasoning of Reason is mandatory for non-contradiction as much as coherent reasoning by contingent minds is mandatory for non-contradiction and for rational engagement with Reason. This aligns well with Aristotle’s notion of “neosis neoseos”. Truth Table Analysis: TTTTT⎪T TTT TTT TT TTT T TTT TT TTT TT TT TTT TTTTF⎪T TTT TTT TT TTT T TFF FT TTT TT TT TTT TTTFT⎪T TTT TTT TT TTT F FTT TT TTT TT TT TTT TTTFF⎪T TTT TTT TT TTT F FTF FT TTT TT TT TTT TTFTT⎪T TTT TFF TF TFF T TTT TF TTT FF TF TFF TTFTF⎪T TTT TFF TF TFF T TFF FT TTT FF TF TFF TTFFT⎪T TTT TFF TF TFF F FTT TF TTT FF TF TFF TTFFF⎪T TTT TFF TF TFF F FTF FT TTT FF TF TFF TFTTT⎪T TFF TTT TF FFT T TTT TF TFF FT TF FFT TFTTF⎪T TFF TTT TF FFT T TFF FT TFF FT TF FFT TFTFT⎪T TFF TTT TF FFT F FTT TF TFF FT TF FFT TFTFF⎪T TFF TTT TF FFT F FTF FT TFF FT TF FFT TFFTT⎪T TFF TFF TT FTF T TTT TF TFF FF TT FTF TFFTF⎪T TFF TFF TT FTF T TFF FT TFF FF TT FTF TFFFT⎪T TFF TFF TT FTF F FTT TF TFF FF TT FTF TFFFF⎪T TFF TFF TT FTF F FTF FT TFF FF TT FTF FTTTT⎪F FTT FTT FT TTT T TTT TF FFT FT FF TTT FTTTF⎪F FTT FTT FT TTT T TFF FT FFT FT FF TTT FTTFT⎪F FTT FTT FT TTT F FTT TF FFT FT FF TTT FTTFF⎪F FTT FTT FT TTT F FTF FT FFT FT FF TTT FTFTT⎪F FTT FTF FT TFF T TTT TF FFT FF FT TFF FTFTF⎪F FTT FTF FT TFF T TFF FT FFT FF FT TFF FTFFT⎪F FTT FTF FT TFF F FTT TF FFT FF FT TFF FTFFF⎪F FTT FTF FT TFF F FTF FT FFT FF FT TFF FFTTT⎪F FTF FTT FT FFT T TTT TF FFF FT FT FFT FFTTF⎪F FTF FTT FT FFT T TFF FT FFF FT FT FFT FFTFT⎪F FTF FTT FT FFT F FTT TF FFF FT FT FFT FFTFF⎪F FTF FTT FT FFT F FTF FT FFF FT FT FFT FFFTT⎪F FTF FTF FT FTF T TTT TF FFF FF FF FTF FFFTF⎪F FTF FTF FT FTF T TFF FT FFF FF FF FTF FFFFT⎪F FTF FTF FT FTF F FTT TF FFF FF FF FTF FFFFF⎪F FTF FTF FT FTF F FTF FT FFF FF FF FTF (VALID) QED

Lean 4 verification and timestamps

The machine formalization date is separate from the original authored work. See the verification record for exact checked scope and any unresolved parts.

Logic-centered continuity

This authored proof is connected to Logic, Logos, God, and the self-evident Ground of Reality, and to the distinct systems 4P Engine, MCB Core, 4P-MCB, and the source-first Canon. Formal proof, empirical evidence, and system-generated records remain separately typed.